pull down to refresh

Not only is that true, but even if you fully trust the federation its still a useless distinction - lnurl, by definition, cannot be non-custodial. Its a single (HTTPS) server that can steal any and all payments to you. They can't take money after you have it, but its not a very interesting distinction IMO.
lnurl, by definition, cannot be non-custodial
It can
You can run the server yourself, then it is self custodial
Senders can also validate the signature in the intended recipient's invoice to ensure it hasn't been swapped (I implemented something pretty similar to this for zaplocker, though I didn't go all the way) -- that also makes it self custodial